The top graph, which represents height vs. time, always has a positive slope, but that slope decreases as x increases. The bottom graph, which represents growth rate vs. time, almost always has a negative slope that increases as x increases.
The minimum height on the height vs. time graph over the interval of [5, 10], from 5 years to 10 years, is 1.042 meters. The maximum height over that same interval is 1.396 meters. By subtracting the minimum height from the maximum height, the change in height was calculated. 1.396 meters minus 1.042 meters equals 0.354 meters, which is the change in height over that interval.
The integral represents the change in height over the interval selected because the derivative of height is growth rate, and when you find the antiderivitive of the derivative over the interval selected, the original change in height over that interval is the result.
The area of the colored region is equal to the difference between the maximum height and the minimum height.
Colin’s adult height is approximately twice his height at age 3, but the assumption that individuals grow most rapidly as teenagers is not supported by the data. According to the growth rate vs. time graph above, Colin’s maximum growth rate was at approximately 6 months old.
The top graph, which represents height vs. time, always has a positive slope, but that slope decreases as x increases. The bottom graph, which represents growth rate vs. time, almost always has a negative slope that increases as x increases.
The minimum height on the height vs. time graph over the interval of [5, 10], from 5 years to 10 years, is 1.042 meters. The maximum height over that same interval is 1.396 meters. By subtracting the minimum height from the maximum height, the change in height was calculated. 1.396 meters minus 1.042 meters equals 0.354 meters, which is the change in height over that interval.
The integral represents the change in height over the interval selected because the derivative of height is growth rate, and when you find the antiderivitive of the derivative over the interval selected, the original change in height over that interval is the result.
The area of the colored region is equal to the difference between the maximum height and the minimum height.
Colin’s adult height is approximately twice his height at age 3, but the assumption that individuals grow most rapidly as teenagers is not supported by the data. According to the growth rate vs. time graph above, Colin’s maximum growth rate was at approximately 6 months old.